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NASA NTRS1999

A Simple Derivation of the Acoustic Boundary Condition in the Presence of Flow

In modeling the noise propagation in a duct of a ducted fan engine, the authors needed the boundary condition satisfied by the acoustic pressure on a lined duct wall in the presence of flow. The results, in the form used by the authors, was derived by M.K. Myers, who presented a formal derivation of a related results by K. Taylor. Here, a brief and simple derivation of the acoustic boundary condition of Myers is given. The main difference in the derivation from that by Myers is that the Gaussian coordinate system (q(exp 1, q(exp 2), q(exp 3)(q(exp 1, q(exp 2), t)) is used to specify the instantaneous position, i.e. Lagrangian variable, of the point on the mean position of the wall with curvilinear (Gaussian) coordinates (q(exp 1), q(exp 2)). Myers uses a locally orthogonal coordinate system which is somewhat less specific than what is used here.

Farassat, F.↗

NASA NTRS1983

Geometric correction process for the Landsat-4 Thematic Mapper

The processing approaches which form the basis of the Landsat-4 Thematic Mapper (TM) geometric correction system are summarized. The correction is accomplished in two phases. In the first phase, correction data are generated. The spacecraft position, TM frame attitude, TM scanning mirror position, and detector sampling are found as a function of time through a combination of flight segment measurements, ground segment modeling, and control point information. The data, along with the earth position and geoid model, are used to determine the earth location for each TM image sample. Then, using map projections, correction data can be generated which define the location of each TM image sample on the output coordinate system. In the second phase, the correction data are used to resample TM detector samples onto the output coordinate system.

Beyer, E. P.↗

NASA NTRS1975

Standing waves at low Mach number laminar bow shocks

Explorer 43 data were used to study 34 bow shock crossings observed from 5 to 16 earth radii upstream of the average bow shock location. Waves with periods of 6 to 130 s having amplitudes up to delta-B/B = 1 were detected. Wave polarization for the low-frequency waves is right-handed in relation to the average field direction when the observer moves from the upstream to downstream direction but is left-handed when the observer moves in the opposite sense. This fact identified the waves as standing whistler waves in the coordinate system of the shock. The waves are in agreement with collisionless low Mach number laminar shock theory. When the measured parameters were used to calculate theoretical wavelengths, the observed wave frequencies could be used to calculate velocities for the shock-wave coordinate system past the spacecraft; such velocities are mostly between 10 and 30 km/s. It is suggested that the higher-frequency propagating whistler waves may evolve from the standing whistler waves through a decay instability.

Fairfield, D. H.↗

NASA NTRS1991

Elastic response of zone axis (001)-oriented PWA 1480 single crystal: The influence of secondary orientation

The influence of secondary orientation on the elastic response of a zone axis (001)-oriented nickel-base single-crystal superalloy, PWA 1480, was investigated under mechanical loading conditions by applying finite element techniques. Elastic stress analyses were performed with a commercially available finite element code. Secondary orientation of the single-crystal superalloy was offset with respect to the global coordinate system in increments from 0 to 90 deg and stresses developed within the single crystal were determined for each loading condition. The results indicated that the stresses were strongly influenced by the angular offset between the secondary crystal orientation and the global coordinate system. The degree of influence was found to vary with the type of loading condition (mechanical, thermal, or combined) imposed on the single-crystal superalloy.

Kalluri, Sreeramesh↗

NASA NTRS1991

Elastic response of (001)-oriented PWA 1480 single crystal - The influence of secondary orientation

Kalluri, Sreeramesh↗

NASA NTRS2009

Terminal Descent Sensor Simulation

Sulcata software simulates the operation of the Mars Science Laboratory (MSL) radar terminal descent sensor (TDS). The program models TDS radar antennas, RF hardware, and digital processing, as well as the physics of scattering from a coherent ground surface. This application is specific to this sensor and is flexible enough to handle end-to-end design validation. Sulcata is a high-fidelity simulation and is used for performance evaluation, anomaly resolution, and design validation. Within the trajectory frame, almost all internal vectors are represented in whatever coordinate system is used to represent platform position. The trajectory frame must be planet-fixed. The platform body frame is specified relative to arbitrary reference points relative to the platform (spacecraft or test vehicle). Its rotation is a function of time from the trajectory coordinate system specified via dynamics input (file for open loop, callback for closed loop). Orientation of the frame relative to the body is arbitrary, but constant over time. The TDS frame must have a constant rotation and translation from the platform body frame specified at run time. The DEM frame has an arbitrary, but time-constant, rotation and translation with respect to the simulation frame specified at run time. It has the same orientation as sigma0 frame, but is possibly translated. Surface sigma0 has the same arbitrary rotation and translation as DEM frame.

Chen, Curtis W.↗

NASA NTRS1980

Geodetic long baseline interferometry research in Canada

The objectives and results of several studies using the Canadian long baseline interferometry system (LBI) are presented. The precision of measurements from radio telescopes at the Algonquin Radio Observatory (ARO), Lake Traverse, Ontario; the Owens Valley Radio Observatory (OVRO), Big Pine, California; and the Chilbolton Observatory (CHIL), Chilbolton, England, is discussed. Also, since LBI is insensitive to the uncertainty in the geocentric gravitational constant, it is a very useful technique for determining the scales of the coordinate systems used by other precise techniques. Beginning in May 1977, a number of LBI observing sessions were accompanied by simultaneous satellite Doppler observations. The baseline components obtained from the satellite Doppler observations were compared to the LBI values. The weighted mean scale bias of the NSWC 9Z-2 satellite Doppler coordinate system relative to the LBI system was found to be 0.42 + or - 0.05 PPM. The weighted mean difference in the origin of longitude was found to be 0.87 sec + or - 0.01 while the difference in declination origin was found to be 0.06 sec + or - 0.01.

Langley, R. B.↗

NASA NTRS2002

Use of Collocated KWAJEX Satellite, Aircraft, and Ground Measurements for Understanding Ambiguities in TRMM Radiometer Rain Profile Algorithm

Coordinated ground, aircraft, and satellite observations are analyzed from the 1999 TRMM Kwajalein Atoll field experiment (KWAJEX) to better understand the relationships between cloud microphysical processes and microwave radiation intensities in the context of physical evaluation of the Level 2 TRMM radiometer rain profile algorithm and uncertainties with its assumed microphysics-radiation relationships. This talk focuses on the results of a multi-dataset analysis based on measurements from KWAJEX surface, air, and satellite platforms to test the hypothesis that uncertainties in the passive microwave radiometer algorithm (TMI 2a12 in the nomenclature of TRMM) are systematically coupled and correlated with the magnitudes of deviation of the assumed 3-dimensional microphysical properties from observed microphysical properties. Re-stated, this study focuses on identifying the weaknesses in the operational TRMM 2a12 radiometer algorithm based on observed microphysics and radiation data in terms of over-simplifications used in its theoretical microphysical underpinnings. The analysis makes use of a common transform coordinate system derived from the measuring capabilities of the aircraft radiometer used to survey the experimental study area, i.e., the 4-channel AMPR radiometer flown on the NASA DC-8 aircraft. Normalized emission and scattering indices derived from radiometer brightness temperatures at the four measuring frequencies enable a 2-dimensional coordinate system that facilities compositing of Kwajalein S-band ground radar reflectivities, ARMAR Ku-band aircraft radar reflectivities, TMI spacecraft radiometer brightness temperatures, PR Ku-band spacecraft radar reflectivities, bulk microphysical parameters derived from the aircraft-mounted cloud microphysics laser probes (including liquid/ice water contents, effective liquid/ice hydrometeor radii, and effective liquid/ice hydrometeor variances), and rainrates derived from any of the individual ground, aircraft, or satellite algorithms applied to the radar or radiometer measurements, or their combination. The results support the study's underlying hypothesis, particularly in context of ice phase processes, in that the cloud regions where the 2a12 algorithm's microphysical database most misrepresents the microphysical conditions as determined by the laser probes, are where retrieved surface rainrates are most erroneous relative to other reference rainrates as determined by ground and aircraft radar. In reaching these conclusions, TMI and PR brightness temperatures and reflectivities have been synthesized from the aircraft AMPR and ARMAR measurements with the analysis conducted in a composite framework to eliminate measurement noise associated with the case study approach and single element volumes obfuscated by heterogeneous beam filling effects. In diagnosing the performance of the 2a12 algorithm, weaknesses have been found in the cloud-radiation database used to provide microphysical guidance to the algorithm for upper cloud ice microphysics. It is also necessary to adjust a fractional convective rainfall factor within the algorithm somewhat arbitrarily to achieve satisfactory algorithm accuracy.

Smith, Eric A.↗

NASA NTRS1998

Contamination Observed on the Passive Optical Sample Assembly (POSA)-1 Experiment

The Passive Optical Sample Assembly-1 (POSA-1), part of the Mir Environmental Effects Payload (MEEP), was designed to study the combined effects of contamination, atomic oxygen, ultraviolet radiation, vacuum, thermal cycling, and other constituents of the space environment on spacecraft materials. The MEEP program is a Phase 1 International Space Station Risk Mitigation Experiment. The payload was attached by EVA to the exterior of the Mir docking module during the Space Shuttle mission STS-76. It was removed during STS-86 after exposure to the Mir environment for 18 months. POSA-1 consists of nearly 400 samples of thermal control paints, chemical conversion coatings, mirrors, optics, and other candidate materials for International Space Station Alpha (ISSA). POSA-1 also flew state-of-the-art materials, such as electrically conductive thermal control coatings developed under contract by IITRI and AZ Technology, and passive instruments for monitoring the atomic oxygen and ultraviolet radiation dose to the experiment. Contamination was detected on the POSA-1 experiment. On the side facing space (-Z(sub B) direction using the Mir coordinate system), visible contamination was observed. The contamination was uniform as would occur from a slow photodeposition process. A very definite film was deposited on the optical samples. The deposition appears to have directionality with definite shadowing effects. On the side facing the main Mr core (+ZB direction using the Mir coordinate system), no visible contamination was noted. Pre- and post-flight characterization of candidate spacecraft materials is discussed, particularly the effect of contamination on total hemispherical spectral reflectance (250 - 2500 nm), infrared emittance, the bi-directional reflectance distribution function (BRDF), and vacuum ultraviolet spectral reflectance. Extensive photography under normal and black light was performed. Results of electron spectroscopy for chemical analysis (ESCA) and Fourier Transform Infrared Analysis (FTIR) on selected samples are also discussed.

Zwiener, James M.↗

NASA NTRS1983

The NCOREL computer program for 3D nonlinear supersonic potential flow computations

An innovative computational technique (NCOREL) was established for the treatment of three dimensional supersonic flows. The method is nonlinear in that it solves the nonconservative finite difference analog of the full potential equation and can predict the formation of supercritical cross flow regions, embedded and bow shocks. The method implicitly computes a conical flow at the apex (R = 0) of a spherical coordinate system and uses a fully implicit marching technique to obtain three dimensional cross flow solutions. This implies that the radial Mach number must remain supersonic. The cross flow solutions are obtained by using type dependent transonic relaxation techniques with the type dependency linked to the character of the cross flow velocity (i.e., subsonic/supersonic). The spherical coordinate system and marching on spherical surfaces is ideally suited to the computation of wing flows at low supersonic Mach numbers due to the elimination of the subsonic axial Mach number problems that exist in other marching codes that utilize Cartesian transverse marching planes.

Siclari, M. J.↗

NASA NTRS1964

Tables for Supersonic Flow Around Right Circular Cones at Small Angle of Attack

The solution of supersonic flow fields by the method of characteristics requires that starting conditions be known. Ferri, in reference 1, developed a method-of-characteristics solution for axially symmetric bodies of revolution at small angles of attack. With computing machinery that is now available, this has become a feasible method for computing the aerodynamic characteristics of bodies near zero angle of attack. For sharp-nosed bodies of revolution, the required starting line may be obtained by computing the flow field about a cone at a small angle of attack. This calculation is readily performed using Stone's theory in reference 2. Some solutions of this theory are available in reference 3. However, the manner in which these results are presented, namely in a wind-fixed coordinate system, makes their use somewhat cumbersome. Additionally, as pointed out in reference 4, the flow component perpendicular to the meridian planes was computed incorrectly. The results contained herein have been computed in the same basic manner as those of reference 3 with the correct velocity normal to the meridian planes. Also, all results have been transferred into the body-fixed coordinate system. Therefore, the values tabulated herein may be used, in conjunction with the respective zero-angle-of-attack results of reference 5, as starting conditions for the method-of-characteristics solution of the flow field about axially symmetric bodies of revolution at small angles of attack. As in the zero-angle-of-attack case (ref. 5) the present results have been computed using the ideal gas value of 1.4 for the ratio of the specific heats of air. Solutions are given for cone angles from 2.5 deg to 30 deg in increments of 2.5 deg. For each cone angle, results were computed for a constant series of free-stream Mach numbers from 1.5 to 20. In addition, a solution was computed which yielded the minimum free-stream Mach number for a completely supersonic conical flow field. For cone angles of 27.5 deg and 30 deg, this minimum free-stream Mach number was above 1.5. Consequently, solutions at this Mach number were not computed for these two cone angles.

SUPERSONIC FLOW↗

NASA NTRS2019

A Streamlined Approach to Spatial Mapping of Complex 3D Thermal Boundary Condition Data

Spatial mapping of 1D, 2D, and particularly 3D thermal boundary condition data is essential for accurate thermal simulation of spacecraft and launch vehicles. This information typically is available in simple ASCII file format but can be problematic to use for thermal simulations. Difficulties that can be encountered include the ability to directly use the available file format, transformation of the data into the desired reference coordinate system in 3D space, and accurate interpolation of the data onto the thermal calculation domain. This paper presents a streamlined approach to spatial mapping of complex unsymmetrical 3D cold wall heat flux data using the fields’ capability in Simcenter3D. A recent example of 3D thermal plume simulation at MSFC will be employed to illustrate the use of text, csv, and Excel files, specifying coordinate systems for transformation of data in 3D space, and use of the various interpolation schemes available for spatial mapping. Spatial boundary condition verification is also very important, and the spacecraft thermal analyst needs effective visualization tools to develop confidence in the boundary condition definitions. Visualization of the spacecraft plume raw field data, the calculated field data, and the interpolated field data onto the thermal calculation domain will be discussed, with a particular focus on real-time viewing of the interpolated data for available interpolation schemes. The objective of this paper is to outline the modeling techniques used with the integrated thermal analysis of a terrestrial lunar lander demonstrator. Specifically, the techniques outlined herein focus on spatial mapping of convective and radiative exhaust plume results from a computational fluid dynamics (CFD) analysis. Two cases were investigated, however, the modeling techniques that were utilized translate to both cases seamlessly. Those two cases were as follows: • Lunar lander demonstrator firing on-pad (worst case). • Lunar lander demonstrator hovering at an elevated position above the launch pad. For the purposes of information control, this paper will focus on the modeling techniques only, using altered or dimensionless data where necessary. BACKGROUND The thermal model examined in this paper is of the lunar lander demonstrator known as XL-1T (terrestrial), born from a collaborative effort between Masten Space Systems (MSS) and NASA, under NASA’s Lunar CATALYST (also known as Lunar Cargo Transportation and Landing by Soft Touchdown) initiative. The lander is a reusable vertical takeoff/vertical landing (VTVL) test bed which is controlled by four throttleable main engines utilizing green hypergolic propellants.

Hawkins, Robert F.↗

NASA NTRS1978

The exact numerical calculation of propeller noise

This paper presents a method for computing the acoustic pressure signature of a propeller due to blade thickness and steady surface pressure loading including the effect of forward motion. The tip helical speed is restricted to subsonic. The formulation is based on the Ffowcs Williams-Hawkings exact result concerning the sound generation by moving bodies. The blade surface is described in a helical coordinate system by the blade angles, positions of the leading and trailing edges along the local pitch helix, and the camber and thickness distributions along the chord. The retarded distance of the moving acoustic source on an element of surface area of the propeller blade is obtained numerically by Newton's method. The surface integration over the propeller blades is carried out in the helical coordinate system using a double Gauss-Legendre formula. Good agreement was found between analytic and experimental results, both in the time and frequency domains. Some samples showing the effects of propeller geometry and tip Mach number on the acoustic signature are included.

Woan, C. J.↗

NASA NTRS1988

A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows

A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streawise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock waves in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.

Goorjian, Peter M.↗

NASA NTRS1988

A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows

A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streamwise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock wave in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.

Goorjian, P. M.↗

NASA NTRS1983

A survey of grid generation techniques in computational fluid dynamics

The use of numerically-generated body-conforming coordinate systems has become well-established in computational fluid dynamics, allowing general codes to be written which can treat boundaries of arbitrary shape. There is now a rapidly increasing interest in the dynamic coupling of the grid with the physical solution so that the grid lines continually move to achieve concentration in regions of strong variation of the physical solution and alignment with shocks, flame fronts, etc. Such adaptive coordinate systems have been developed using a variety of techniques for sensing and reacting to the developing regions of concentration and/or alignment. This paper reviews the techniques and applications of these dynamically adaptive systems and other systems.

Thompson, J. F.↗

NASA NTRS1978

Determining crustal strain rates with a spaceborne geodynamics ranging system. 2: Station coordinate analysis

The use of a spaceborne geodynamics ranging system for determining crustal strain rates is analyzed. The use of site coordinates rather than intersite baseline distances for the strain rate determinations is emphasized. After discussing the analytical techniques which are to be employed, numerical results are presented which suggest that the use of site coordinates would result in a 20-70% improvement in the precision of the deduced values of straining. Precision of a few parts in 10 to the 9th power would be achievable with simple geometrics and a decade or two of measurements; precisions of a few parts in 10 to the 8th power would be achievable in a few years. A consideration of possible correlations among the derived target site coordinates leads to the conclusion that, with the proper choice of coordinate systems, the correlations can be made small and non-detrimental to the strain rate determinations.

Cohen, S. C.↗

NASA NTRS2007

Semianalytical Propagation of Satellite Orbits about an Arbitrary Central Body

Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness

Cefola, Paul J.↗